Assignment8-Coexpression
Goal: We want to understand how plants connect the upstream perception of environmental signals (in this case the presence of neighbors) and how this information cascades through the biological network of the organism to affect the downstream outputs of physiological and developmental changes, eg. gene expression
upstream input to downstream output
Network intuition example
cities <- read.delim("us_cities.txt", row.names=1) # be sure to change the path
cities## BOS NY DC MIA CHI SEA SF LA DEN
## BOS 0 206 429 1504 963 2976 3095 2979 1949
## NY 206 0 233 1308 802 2815 2934 2786 1771
## DC 429 233 0 1075 671 2684 2799 2631 1616
## MIA 1504 1308 1075 0 1329 3273 3053 2687 2037
## CHI 963 802 671 1329 0 2013 2142 2054 996
## SEA 2976 2815 2684 3273 2013 0 808 1131 1307
## SF 3095 2934 2799 3053 2142 808 0 379 1235
## LA 2979 2786 2631 2687 2054 1131 379 0 1059
## DEN 1949 1771 1616 2037 996 1307 1235 1059 0choose distance within 1500 miles, assigned to be 1
distance outside 1500 miles, assigned to be 0
create adjacency matrix
cities_mat <- cities < 1500 # leave original matrix intact
diag(cities_mat) <- 0 # we do not have to fly within each of cities; automatically change matrix to 1/0 form because T/F (1/0)
cities_mat # check out the adjacency matrix## BOS NY DC MIA CHI SEA SF LA DEN
## BOS 0 1 1 0 1 0 0 0 0
## NY 1 0 1 1 1 0 0 0 0
## DC 1 1 0 1 1 0 0 0 0
## MIA 0 1 1 0 1 0 0 0 0
## CHI 1 1 1 1 0 0 0 0 1
## SEA 0 0 0 0 0 0 1 1 1
## SF 0 0 0 0 0 1 0 1 1
## LA 0 0 0 0 0 1 1 0 1
## DEN 0 0 0 0 1 1 1 1 0exercise 1:
rowSums(cities_mat)## BOS NY DC MIA CHI SEA SF LA DEN
## 3 4 4 3 5 3 3 3 4colSums(cities_mat)## BOS NY DC MIA CHI SEA SF LA DEN
## 3 4 4 3 5 3 3 3 4Chicago has the largest number, so it is the most highly connected
Try extend cities range to 2000
cities_mat_2000 <- cities < 2000 # leave original matrix intact
diag(cities_mat_2000) <- 0 # we do not have to fly within each of cities; automatically change matrix to 1/0 form because T/F (1/0)
cities_mat_2000 # check out the adjacency matrix## BOS NY DC MIA CHI SEA SF LA DEN
## BOS 0 1 1 1 1 0 0 0 1
## NY 1 0 1 1 1 0 0 0 1
## DC 1 1 0 1 1 0 0 0 1
## MIA 1 1 1 0 1 0 0 0 0
## CHI 1 1 1 1 0 0 0 0 1
## SEA 0 0 0 0 0 0 1 1 1
## SF 0 0 0 0 0 1 0 1 1
## LA 0 0 0 0 0 1 1 0 1
## DEN 1 1 1 0 1 1 1 1 0rowSums(cities_mat_2000)## BOS NY DC MIA CHI SEA SF LA DEN
## 5 5 5 4 5 3 3 3 7yes it changes to Denver. because Denver is in the midwest where is more ajacent to either west coast cities or east coast cities, within 2000 miles.
Plot network
library(igraph) # load package##
## Attaching package: 'igraph'## The following objects are masked from 'package:stats':
##
## decompose, spectrum## The following object is masked from 'package:base':
##
## union# make sure to use the 2000 mile distance cutoff
cities_graph2 <- graph.adjacency(cities_mat_2000, mode = "undirected")
plot.igraph(cities_graph2)
exercise 2:
total # of nodes: 9
total # of edges: 20 (look at the cities_graph2 file, near the title) or
sum(cities_mat_2000)/2## [1] 20Exercise 3:
recalculate using cutoff of 2300
cities_mat_2300 <- cities < 2300 # leave original matrix intact
diag(cities_mat_2300) <- 0 # we do not have to fly within each of cities; automatically change matrix to 1/0 form because T/F (1/0)
cities_mat_2300 # check out the adjacency matrix## BOS NY DC MIA CHI SEA SF LA DEN
## BOS 0 1 1 1 1 0 0 0 1
## NY 1 0 1 1 1 0 0 0 1
## DC 1 1 0 1 1 0 0 0 1
## MIA 1 1 1 0 1 0 0 0 1
## CHI 1 1 1 1 0 1 1 1 1
## SEA 0 0 0 0 1 0 1 1 1
## SF 0 0 0 0 1 1 0 1 1
## LA 0 0 0 0 1 1 1 0 1
## DEN 1 1 1 1 1 1 1 1 0sum(cities_mat_2300)/2## [1] 2424 edges obtained
gene problem
We will define each gene as a node and the edges between the nodes as some value that we can calculate to make an adjacency matrix
We can use similarity in gene expression values to measure the biological distance between genes. Genes that are expressed in more similar patterns should be closer.
load data
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.2.1 ──## ✔ ggplot2 2.2.1 ✔ purrr 0.2.4
## ✔ tibble 1.4.2 ✔ dplyr 0.7.4
## ✔ tidyr 0.8.0 ✔ stringr 1.3.0
## ✔ readr 1.1.1 ✔ forcats 0.3.0## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::as_data_frame() masks tibble::as_data_frame(), igraph::as_data_frame()
## ✖ purrr::compose() masks igraph::compose()
## ✖ tidyr::crossing() masks igraph::crossing()
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::groups() masks igraph::groups()
## ✖ dplyr::lag() masks stats::lag()
## ✖ purrr::simplify() masks igraph::simplify()# make sure to change the path to where you downloaded this using wget
DE_genes <- read_csv("DEgenes_GxE.csv")## Parsed with column specification:
## cols(
## GeneID = col_character(),
## logFC = col_double(),
## logCPM = col_double(),
## LR = col_double(),
## PValue = col_double(),
## FDR = col_double()
## )head(DE_genes) #check out the data## # A tibble: 6 x 6
## GeneID logFC logCPM LR PValue FDR
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Bra010821 6.66 6.04 153. 3.54e-35 8.51e-31
## 2 Bra033034 -4.64 6.61 71.3 3.13e-17 3.76e-13
## 3 Bra035334 -4.14 4.67 68.3 1.37e-16 1.10e-12
## 4 Bra003598 -4.89 3.90 54.2 1.85e-13 1.11e- 9
## 5 Bra016182 7.71 6.33 49.6 1.87e-12 9.00e- 9
## 6 Bra013164 4.10 9.33 47.9 4.38e-12 1.76e- 8# make sure to change the path to where you downloaded this using wget
brass_voom_E <- read_csv("voom_transform_brassica.csv")## Parsed with column specification:
## cols(
## .default = col_double(),
## GeneID = col_character()
## )## See spec(...) for full column specifications.brass_voom_E[,-c(38,42,46)] # remove questionable library columns## # A tibble: 29,791 x 46
## GeneID IMB211_DP_1_INTERNODE IMB211_DP_1_LEAF IMB211_DP_1_PETIOLE
## <chr> <dbl> <dbl> <dbl>
## 1 Bra000002 1.86 -3.43 4.22
## 2 Bra000003 5.37 6.35 6.52
## 3 Bra000004 0.624 2.00 1.99
## 4 Bra000005 5.90 4.85 5.75
## 5 Bra000006 4.35 3.20 4.73
## 6 Bra000007 1.18 1.53 2.70
## 7 Bra000008 1.86 1.43 3.36
## 8 Bra000009 5.56 6.37 6.43
## 9 Bra000011 3.99 3.31 4.24
## 10 Bra000012 3.20 2.55 3.47
## # ... with 29,781 more rows, and 42 more variables:
## # IMB211_DP_1_SILIQUE <dbl>, IMB211_DP_2_INTERNODE <dbl>,
## # IMB211_DP_2_LEAF <dbl>, IMB211_DP_2_PETIOLE <dbl>,
## # IMB211_DP_2_SILIQUE <dbl>, IMB211_DP_3_INTERNODE <dbl>,
## # IMB211_DP_3_LEAF <dbl>, IMB211_DP_3_PETIOLE <dbl>,
## # IMB211_DP_3_SILIQUE <dbl>, IMB211_NDP_1_INTERNODE <dbl>,
## # IMB211_NDP_1_LEAF <dbl>, IMB211_NDP_1_PETIOLE <dbl>,
## # IMB211_NDP_1_SILIQUE <dbl>, IMB211_NDP_2_INTERNODE <dbl>,
## # IMB211_NDP_2_LEAF <dbl>, IMB211_NDP_2_PETIOLE <dbl>,
## # IMB211_NDP_2_SILIQUE <dbl>, IMB211_NDP_3_INTERNODE <dbl>,
## # IMB211_NDP_3_LEAF <dbl>, IMB211_NDP_3_PETIOLE <dbl>,
## # IMB211_NDP_3_SILIQUE <dbl>, R500_DP_1_INTERNODE <dbl>,
## # R500_DP_1_LEAF <dbl>, R500_DP_1_PETIOLE <dbl>,
## # R500_DP_1_SILIQUE <dbl>, R500_DP_2_INTERNODE <dbl>,
## # R500_DP_2_LEAF <dbl>, R500_DP_2_PETIOLE <dbl>,
## # R500_DP_2_SILIQUE <dbl>, R500_DP_3_INTERNODE <dbl>,
## # R500_DP_3_LEAF <dbl>, R500_DP_3_PETIOLE <dbl>,
## # R500_DP_3_SILIQUE <dbl>, R500_NDP_1_LEAF <dbl>,
## # R500_NDP_1_PETIOLE <dbl>, R500_NDP_1_SILIQUE <dbl>,
## # R500_NDP_2_LEAF <dbl>, R500_NDP_2_PETIOLE <dbl>,
## # R500_NDP_2_SILIQUE <dbl>, R500_NDP_3_LEAF <dbl>,
## # R500_NDP_3_PETIOLE <dbl>, R500_NDP_3_SILIQUE <dbl>head(brass_voom_E)## # A tibble: 6 x 49
## GeneID IMB211_DP_1_INTERNODE IMB211_DP_1_LEAF IMB211_DP_1_PETIOLE
## <chr> <dbl> <dbl> <dbl>
## 1 Bra000002 1.86 -3.43 4.22
## 2 Bra000003 5.37 6.35 6.52
## 3 Bra000004 0.624 2.00 1.99
## 4 Bra000005 5.90 4.85 5.75
## 5 Bra000006 4.35 3.20 4.73
## 6 Bra000007 1.18 1.53 2.70
## # ... with 45 more variables: IMB211_DP_1_SILIQUE <dbl>,
## # IMB211_DP_2_INTERNODE <dbl>, IMB211_DP_2_LEAF <dbl>,
## # IMB211_DP_2_PETIOLE <dbl>, IMB211_DP_2_SILIQUE <dbl>,
## # IMB211_DP_3_INTERNODE <dbl>, IMB211_DP_3_LEAF <dbl>,
## # IMB211_DP_3_PETIOLE <dbl>, IMB211_DP_3_SILIQUE <dbl>,
## # IMB211_NDP_1_INTERNODE <dbl>, IMB211_NDP_1_LEAF <dbl>,
## # IMB211_NDP_1_PETIOLE <dbl>, IMB211_NDP_1_SILIQUE <dbl>,
## # IMB211_NDP_2_INTERNODE <dbl>, IMB211_NDP_2_LEAF <dbl>,
## # IMB211_NDP_2_PETIOLE <dbl>, IMB211_NDP_2_SILIQUE <dbl>,
## # IMB211_NDP_3_INTERNODE <dbl>, IMB211_NDP_3_LEAF <dbl>,
## # IMB211_NDP_3_PETIOLE <dbl>, IMB211_NDP_3_SILIQUE <dbl>,
## # R500_DP_1_INTERNODE <dbl>, R500_DP_1_LEAF <dbl>,
## # R500_DP_1_PETIOLE <dbl>, R500_DP_1_SILIQUE <dbl>,
## # R500_DP_2_INTERNODE <dbl>, R500_DP_2_LEAF <dbl>,
## # R500_DP_2_PETIOLE <dbl>, R500_DP_2_SILIQUE <dbl>,
## # R500_DP_3_INTERNODE <dbl>, R500_DP_3_LEAF <dbl>,
## # R500_DP_3_PETIOLE <dbl>, R500_DP_3_SILIQUE <dbl>,
## # R500_NDP_1_INTERNODE <dbl>, R500_NDP_1_LEAF <dbl>,
## # R500_NDP_1_PETIOLE <dbl>, R500_NDP_1_SILIQUE <dbl>,
## # R500_NDP_2_INTERNODE <dbl>, R500_NDP_2_LEAF <dbl>,
## # R500_NDP_2_PETIOLE <dbl>, R500_NDP_2_SILIQUE <dbl>,
## # R500_NDP_3_INTERNODE <dbl>, R500_NDP_3_LEAF <dbl>,
## # R500_NDP_3_PETIOLE <dbl>, R500_NDP_3_SILIQUE <dbl>GxE_counts <- DE_genes %>% select(GeneID) %>% left_join(brass_voom_E) #get count data specifically for the GxE genes## Joining, by = "GeneID"head(GxE_counts)## # A tibble: 6 x 49
## GeneID IMB211_DP_1_INTERNODE IMB211_DP_1_LEAF IMB211_DP_1_PETIOLE
## <chr> <dbl> <dbl> <dbl>
## 1 Bra010821 -3.46 1.70 0.134
## 2 Bra033034 8.32 -3.43 -1.24
## 3 Bra035334 6.01 2.62 2.81
## 4 Bra003598 4.05 6.09 5.10
## 5 Bra016182 -0.00370 -1.84 5.38
## 6 Bra013164 4.25 -3.43 2.64
## # ... with 45 more variables: IMB211_DP_1_SILIQUE <dbl>,
## # IMB211_DP_2_INTERNODE <dbl>, IMB211_DP_2_LEAF <dbl>,
## # IMB211_DP_2_PETIOLE <dbl>, IMB211_DP_2_SILIQUE <dbl>,
## # IMB211_DP_3_INTERNODE <dbl>, IMB211_DP_3_LEAF <dbl>,
## # IMB211_DP_3_PETIOLE <dbl>, IMB211_DP_3_SILIQUE <dbl>,
## # IMB211_NDP_1_INTERNODE <dbl>, IMB211_NDP_1_LEAF <dbl>,
## # IMB211_NDP_1_PETIOLE <dbl>, IMB211_NDP_1_SILIQUE <dbl>,
## # IMB211_NDP_2_INTERNODE <dbl>, IMB211_NDP_2_LEAF <dbl>,
## # IMB211_NDP_2_PETIOLE <dbl>, IMB211_NDP_2_SILIQUE <dbl>,
## # IMB211_NDP_3_INTERNODE <dbl>, IMB211_NDP_3_LEAF <dbl>,
## # IMB211_NDP_3_PETIOLE <dbl>, IMB211_NDP_3_SILIQUE <dbl>,
## # R500_DP_1_INTERNODE <dbl>, R500_DP_1_LEAF <dbl>,
## # R500_DP_1_PETIOLE <dbl>, R500_DP_1_SILIQUE <dbl>,
## # R500_DP_2_INTERNODE <dbl>, R500_DP_2_LEAF <dbl>,
## # R500_DP_2_PETIOLE <dbl>, R500_DP_2_SILIQUE <dbl>,
## # R500_DP_3_INTERNODE <dbl>, R500_DP_3_LEAF <dbl>,
## # R500_DP_3_PETIOLE <dbl>, R500_DP_3_SILIQUE <dbl>,
## # R500_NDP_1_INTERNODE <dbl>, R500_NDP_1_LEAF <dbl>,
## # R500_NDP_1_PETIOLE <dbl>, R500_NDP_1_SILIQUE <dbl>,
## # R500_NDP_2_INTERNODE <dbl>, R500_NDP_2_LEAF <dbl>,
## # R500_NDP_2_PETIOLE <dbl>, R500_NDP_2_SILIQUE <dbl>,
## # R500_NDP_3_INTERNODE <dbl>, R500_NDP_3_LEAF <dbl>,
## # R500_NDP_3_PETIOLE <dbl>, R500_NDP_3_SILIQUE <dbl>GxE_counts <- GxE_counts %>% column_to_rownames("GeneID") %>% as.matrix(GxE_counts) # some of the downstream steps require a data matrix## Warning: Setting row names on a tibble is deprecated.## Warning in if (rownames.force %in% FALSE) NULL else if (rownames.force %in
## % : the condition has length > 1 and only the first element will be used## Warning in if (rownames.force %in% TRUE) row.names(x) else if
## (.row_names_info(x) <= : the condition has length > 1 and only the first
## element will be usedhead(GxE_counts[,1:6])## IMB211_DP_1_INTERNODE IMB211_DP_1_LEAF IMB211_DP_1_PETIOLE
## Bra010821 -3.463127655 1.701664 0.1337041
## Bra033034 8.321098205 -3.427619 -1.2448076
## Bra035334 6.006514162 2.616775 2.8083038
## Bra003598 4.052572183 6.092017 5.0986003
## Bra016182 -0.003696037 -1.842657 5.3816316
## Bra013164 4.251117862 -3.427619 2.6427177
## IMB211_DP_1_SILIQUE IMB211_DP_2_INTERNODE IMB211_DP_2_LEAF
## Bra010821 2.4624596 -1.601140 2.942148
## Bra033034 0.7124379 8.236488 -3.597011
## Bra035334 1.7765682 6.769547 1.612442
## Bra003598 1.5009338 4.281503 5.753928
## Bra016182 1.7765682 -1.601140 -2.012048
## Bra013164 6.5337770 5.353056 -2.012048start with 5 genes subsets
GxE_subset <- GxE_counts[1:5,] # first five genes
# create correlation matrix
GxE_cor <- cor(t(GxE_subset)) # gene across tissue, each gene is a variable, use gene to describe each sample
GxE_cor %>% round(3) # round to three decimal points## Bra010821 Bra033034 Bra035334 Bra003598 Bra016182
## Bra010821 1.000 0.368 0.254 0.360 0.578
## Bra033034 0.368 1.000 0.642 0.101 0.386
## Bra035334 0.254 0.642 1.000 0.649 0.534
## Bra003598 0.360 0.101 0.649 1.000 0.401
## Bra016182 0.578 0.386 0.534 0.401 1.000# set diagonal to 0
diag(GxE_cor) <- 0
GxE_cor## Bra010821 Bra033034 Bra035334 Bra003598 Bra016182
## Bra010821 0.0000000 0.3680247 0.2539597 0.3603182 0.5784638
## Bra033034 0.3680247 0.0000000 0.6421482 0.1014876 0.3863322
## Bra035334 0.2539597 0.6421482 0.0000000 0.6492046 0.5344374
## Bra003598 0.3603182 0.1014876 0.6492046 0.0000000 0.4008675
## Bra016182 0.5784638 0.3863322 0.5344374 0.4008675 0.0000000Rank the correlation
# 2 means cols, 1 means rows
GxE_rank <- apply(GxE_cor,2,function(x) rank(-abs(x)))
# rank for each column from high to low
GxE_rank## Bra010821 Bra033034 Bra035334 Bra003598 Bra016182
## Bra010821 5 3 4 3 1
## Bra033034 2 5 2 4 4
## Bra035334 4 1 5 1 2
## Bra003598 3 4 1 5 3
## Bra016182 1 2 3 2 5Exercise 4:
(A) “1” in the [“Bra035334”, “Bra033034”] cell means these two genes have the greatest correlation.
- yes they have different value. because we are ranking for every column. In each column, the ranking for particular pair can be different depending on the values within that column.
compare pairwise mutual ranks (average ranks)
GxE_MR <- sqrt(GxE_rank * t(GxE_rank))
GxE_MR## Bra010821 Bra033034 Bra035334 Bra003598 Bra016182
## Bra010821 5.00000 2.449490 4.000000 3.00000 1.000000
## Bra033034 2.44949 5.000000 1.414214 4.00000 2.828427
## Bra035334 4.00000 1.414214 5.000000 1.00000 2.449490
## Bra003598 3.00000 4.000000 1.000000 5.00000 2.449490
## Bra016182 1.00000 2.828427 2.449490 2.44949 5.000000- no, their values are the same. because we are doing above is to multiply the different ranking for each given pair to their counterpart different ranking, such that they will agree on the ranking score. then take the average to obtain the average value which is also the same for each pair.
Define edge: rank less or equal than 2
genes_adj_MR2 <- GxE_MR <= 2
diag(genes_adj_MR2) <- 0
genes_adj_MR2## Bra010821 Bra033034 Bra035334 Bra003598 Bra016182
## Bra010821 0 0 0 0 1
## Bra033034 0 0 1 0 0
## Bra035334 0 1 0 1 0
## Bra003598 0 0 1 0 0
## Bra016182 1 0 0 0 0- Bra035334 is connected to Bra033034 and Bra003598
Exercise 6
genes_adj_MR3
GxE_cor <- cor(t(GxE_counts))
GxE_cor %>% round(3) # round to three decimal points## Bra010821 Bra033034 Bra035334 Bra003598
## Bra010821 1.000 0.368 0.254 0.360
## Bra033034 0.368 1.000 0.642 0.101
## Bra035334 0.254 0.642 1.000 0.649
## Bra003598 0.360 0.101 0.649 1.000
## Bra016182 0.578 0.386 0.534 0.401
## Bra013164 0.702 0.657 0.271 -0.051
## Bra009406 0.788 0.520 0.402 0.360
## Bra033856 0.502 0.854 0.729 0.302
## Bra011196 0.662 0.330 0.665 0.696
## Bra041036 0.327 0.838 0.856 0.458
## Bra011170 0.421 0.447 0.747 0.496
## Bra037664 0.572 0.842 0.763 0.411
## Bra002697 0.755 0.492 0.665 0.702
## Bra025547 0.068 0.095 0.691 0.819
## Bra016316 0.521 0.833 0.753 0.382
## Bra019741 0.669 0.628 0.446 0.232
## Bra020500 0.814 0.546 0.203 0.046
## Bra005176 0.869 0.525 0.315 0.187
## Bra036334 0.639 0.704 0.267 -0.141
## Bra013340 0.470 0.539 0.832 0.755
## Bra011670 0.395 0.579 0.910 0.776
## Bra038908 0.779 0.540 0.245 0.121
## Bra027181 0.606 0.802 0.345 -0.111
## Bra018722 0.111 0.158 0.740 0.796
## Bra002896 0.570 0.792 0.710 0.372
## Bra010292 0.302 0.708 0.721 0.244
## Bra021913 0.393 0.608 0.844 0.621
## Bra011195 0.628 0.633 0.639 0.402
## Bra007907_Bra007908_Bra007909 0.271 0.630 0.927 0.642
## Bra027700 0.235 0.372 0.825 0.714
## Bra036607 0.357 0.633 0.907 0.674
## Bra002515 0.706 0.761 0.675 0.511
## Bra031658 0.558 0.635 0.741 0.451
## Bra004810 0.413 0.885 0.699 0.220
## Bra005070 0.221 0.263 0.809 0.809
## Bra035502 0.824 0.595 0.384 0.201
## Bra004892 0.644 0.729 0.715 0.371
## Bra018386 0.517 0.467 0.742 0.656
## Bra040840 0.765 0.664 0.649 0.559
## Bra024269 0.308 0.347 0.711 0.507
## Bra040801 0.080 0.194 0.702 0.659
## Bra017219 0.289 0.809 0.890 0.430
## Bra022378 0.250 0.197 0.782 0.887
## Bra006092 0.179 0.612 0.776 0.280
## Bra032375 0.730 0.684 0.653 0.362
## Bra024197 0.502 0.900 0.791 0.364
## Bra023827 0.577 0.875 0.798 0.426
## Bra021506 0.726 0.750 0.543 0.236
## Bra036155 0.807 0.680 0.309 0.048
## Bra013676_Bra013677 0.347 0.455 0.857 0.806
## Bra036852 0.773 0.692 0.538 0.326
## Bra005071 0.209 0.280 0.815 0.790
## Bra014819 0.872 0.511 0.336 0.286
## Bra013682 0.322 0.233 0.775 0.941
## Bra013628 0.373 0.583 0.916 0.710
## Bra037283 0.194 0.428 0.809 0.724
## Bra016610 0.471 0.676 0.708 0.420
## Bra011606 0.626 0.798 0.515 0.126
## Bra004130 0.379 0.418 0.798 0.792
## Bra036217 0.428 0.768 0.907 0.588
## Bra015896 0.590 0.878 0.770 0.439
## Bra022342 0.405 0.934 0.775 0.289
## Bra005227 0.045 0.184 0.646 0.620
## Bra031068 0.665 0.736 0.702 0.363
## Bra006273 0.797 0.677 0.407 0.137
## Bra020646 -0.059 0.417 0.552 0.183
## Bra017113 0.678 0.562 0.418 0.147
## Bra034676 0.103 0.301 0.773 0.702
## Bra006683 0.580 0.884 0.705 0.318
## Bra025028 0.529 0.435 0.758 0.824
## Bra024102 0.265 0.552 0.826 0.419
## Bra003687 0.746 0.696 0.500 0.316
## Bra011132 0.624 0.895 0.730 0.311
## Bra030671 0.338 0.824 0.888 0.487
## Bra035634 0.143 0.688 0.575 0.021
## Bra015961 0.384 0.357 0.784 0.828
## Bra023460 0.732 0.826 0.540 0.185
## Bra029614 0.878 0.567 0.430 0.394
## Bra009136 0.719 0.675 0.728 0.461
## Bra012492 0.815 0.681 0.555 0.366
## Bra003126 0.467 0.802 0.863 0.538
## Bra008302 0.593 0.607 0.573 0.249
## Bra006291 0.629 0.799 0.580 0.129
## Bra030155 0.844 0.550 0.350 0.317
## Bra000111 0.688 0.591 0.367 0.071
## Bra007141 0.889 0.453 0.337 0.361
## Bra004735 0.638 0.712 0.504 0.172
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## Bra019095 0.602 0.858 0.822 0.889
## Bra016683 0.604 0.637 0.539 0.266
## Bra016964 0.875 0.615 0.834 0.626
## Bra017160 0.320 0.647 0.589 0.500
## Bra002189 0.277 0.595 0.643 0.481
## Bra029880 0.759 0.707 0.685 0.501
## Bra013684 0.817 0.458 0.600 0.365
## Bra033822 0.642 0.739 0.825 0.614
## Bra031841 0.536 0.789 0.755 0.844
## Bra038746 0.260 0.833 0.643 0.761
## Bra012218 0.141 0.615 0.506 0.654
## Bra023383 0.491 0.849 0.713 0.685
## Bra001819 0.522 0.809 0.710 0.780
## Bra030429 0.345 0.736 0.530 0.722
## Bra001774 0.598 0.674 0.535 0.307
## Bra020672 0.395 0.803 0.665 0.576
## Bra009854 0.698 0.585 0.615 0.453
## Bra023576 0.302 0.792 0.667 0.915
## Bra027940 0.467 0.542 0.602 0.343
## Bra007886 0.653 0.404 0.615 0.579
## Bra029387 0.227 0.614 0.624 0.922
## Bra038567 0.819 0.700 0.843 0.625
## Bra019265 0.823 0.600 0.725 0.506
## Bra032747 0.732 0.596 0.721 0.417
## Bra003670 0.602 0.486 0.512 0.233
## Bra037877 0.481 0.578 0.621 0.416
## Bra001921 0.463 0.466 0.570 0.460
## Bra035015 0.437 0.692 0.702 0.802
## Bra019398 0.137 0.574 0.612 0.852
## Bra038899 0.603 0.278 0.614 0.577
## Bra035778 0.217 0.661 0.663 0.830
## Bra029414 0.768 0.528 0.664 0.332
## Bra029039 0.673 0.711 0.815 0.720
## Bra006985 0.470 0.807 0.644 0.763
## Bra011349 0.025 0.539 0.508 0.761
## Bra026022 0.645 0.741 0.799 0.768
## Bra015704 0.832 0.683 0.869 0.615
## Bra037731 0.528 0.489 0.619 0.408
## Bra020799 0.333 0.862 0.793 0.915
## Bra035641 0.738 0.796 0.894 0.780
## Bra024935 0.291 0.778 0.704 0.833
## Bra023130 0.926 0.490 0.704 0.380
## Bra001642 0.239 0.822 0.641 0.768
## Bra010085 0.767 0.801 0.887 0.790
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## Bra025359 0.131 0.742 0.577 0.735
## Bra034030 0.775 0.684 0.789 0.643
## Bra008371 0.803 0.729 0.851 0.667
## Bra009840 0.238 0.790 0.615 0.694
## Bra013657 0.910 0.559 0.729 0.492
## Bra015694 0.460 0.884 0.763 0.871
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## Bra022827 0.771 0.735 0.725 0.508
## Bra018209 0.711 0.729 0.916 0.840
## Bra024459 0.735 0.446 0.649 0.311
## Bra016498 0.630 0.763 0.735 0.707
## Bra028150 0.485 0.796 0.732 0.750
## Bra038785 0.847 0.514 0.722 0.424
## Bra023802 0.680 0.829 0.856 0.716
## Bra006293 0.502 0.843 0.778 0.659
## Bra028523 0.781 0.610 0.726 0.509
## Bra000754 0.858 0.599 0.795 0.524
## Bra038321 0.480 0.847 0.723 0.720
## Bra019742 0.005 0.387 0.382 0.526
## Bra031771 0.337 0.711 0.730 0.805
## Bra019357 0.847 0.706 0.794 0.537
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## Bra024675 0.726 0.782 0.813 0.538
## Bra008780 0.391 0.791 0.552 0.495
## Bra010283 0.865 0.473 0.679 0.331
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## Bra005469 0.522 0.660 0.525 0.408
## Bra012607 0.091 0.804 0.561 0.779
## Bra034140 0.546 0.814 0.812 0.645
## Bra000534 0.704 0.836 0.841 0.865
## Bra012597 0.586 0.815 0.802 0.585
## Bra028400 0.415 0.764 0.667 0.553
## Bra030116 0.405 0.831 0.770 0.786
## Bra004581 0.080 0.628 0.473 0.628
## Bra009182 1.000 0.512 0.703 0.398
## Bra101149 0.512 1.000 0.820 0.762
## Bra027206 0.703 0.820 1.000 0.790
## Bra006173 0.398 0.762 0.790 1.000# set diagonal to 0
diag(GxE_cor) <- 0
GxE_cor## Bra010821 Bra033034 Bra035334
## Bra010821 0.000000000 0.36802466 0.2539597
## Bra033034 0.368024662 0.00000000 0.6421482
## Bra035334 0.253959698 0.64214820 0.0000000
## Bra003598 0.360318245 0.10148761 0.6492046
## Bra016182 0.578463805 0.38633216 0.5344374
## Bra013164 0.701922906 0.65733992 0.2707677
## Bra009406 0.788211446 0.51996506 0.4016402
## Bra033856 0.502384233 0.85390023 0.7287787
## Bra011196 0.661843633 0.33016017 0.6651785
## Bra041036 0.327030441 0.83845984 0.8561854
## Bra011170 0.420648236 0.44741908 0.7474603
## Bra037664 0.571780218 0.84238478 0.7627496
## Bra002697 0.755198432 0.49151558 0.6649436
## Bra025547 0.068233913 0.09538181 0.6905676
## Bra016316 0.521202715 0.83300626 0.7534665
## Bra019741 0.668606126 0.62839721 0.4461170
## Bra020500 0.813910724 0.54588662 0.2032412
## Bra005176 0.868588136 0.52524576 0.3152088
## Bra036334 0.639271807 0.70404132 0.2671752
## Bra013340 0.470226746 0.53864619 0.8318888
## Bra011670 0.395024130 0.57928579 0.9098637
## Bra038908 0.779460424 0.53978272 0.2452793
## Bra027181 0.605907956 0.80200806 0.3452242
## Bra018722 0.110646216 0.15781444 0.7395490
## Bra002896 0.570098267 0.79153925 0.7096854
## Bra010292 0.302374935 0.70832555 0.7213022
## Bra021913 0.392907454 0.60758902 0.8443770
## Bra011195 0.627926987 0.63331934 0.6387829
## Bra007907_Bra007908_Bra007909 0.271351504 0.62970324 0.9271573
## Bra027700 0.235408651 0.37169345 0.8252675
## Bra036607 0.357448030 0.63270804 0.9065435
## Bra002515 0.705620123 0.76148850 0.6745810
## Bra031658 0.558433192 0.63463357 0.7410852
## Bra004810 0.412737292 0.88502222 0.6992285
## Bra005070 0.220846175 0.26327553 0.8094990
## Bra035502 0.824126316 0.59511353 0.3839787
## Bra004892 0.643958650 0.72886527 0.7153433
## Bra018386 0.517432034 0.46727877 0.7418630
## Bra040840 0.765219048 0.66448423 0.6489280
## Bra024269 0.308270898 0.34735308 0.7114072
## Bra040801 0.079944553 0.19407273 0.7019668
## Bra017219 0.288945490 0.80881545 0.8895836
## Bra022378 0.250336368 0.19709022 0.7820201
## Bra006092 0.178998785 0.61233033 0.7762987
## Bra032375 0.730407202 0.68441005 0.6533398
## Bra024197 0.501950349 0.89969566 0.7905486
## Bra023827 0.577497416 0.87530747 0.7982715
## Bra021506 0.726311415 0.75000744 0.5434743
## Bra036155 0.806822791 0.68021058 0.3088956
## Bra013676_Bra013677 0.346652721 0.45454020 0.8573228
## Bra036852 0.773011820 0.69200751 0.5375481
## Bra005071 0.209093297 0.28048291 0.8154040
## Bra014819 0.871853494 0.51112153 0.3357771
## Bra013682 0.321923965 0.23324208 0.7748168
## Bra013628 0.373343306 0.58305656 0.9162302
## Bra037283 0.193951211 0.42758187 0.8093744
## Bra016610 0.470678634 0.67571069 0.7081446
## Bra011606 0.625545317 0.79821176 0.5150432
## Bra004130 0.379093883 0.41812114 0.7978575
## Bra036217 0.427904209 0.76807220 0.9072100
## Bra015896 0.589568145 0.87751611 0.7701026
## Bra022342 0.405025290 0.93365320 0.7753101
## Bra005227 0.044714412 0.18430873 0.6463718
## Bra031068 0.664672404 0.73606319 0.7023010
## Bra006273 0.797429454 0.67704665 0.4070376
## Bra020646 -0.058902076 0.41734848 0.5516178
## Bra017113 0.678399413 0.56177418 0.4184527
## Bra034676 0.102763986 0.30100113 0.7728659
## Bra006683 0.580037064 0.88438754 0.7045132
## Bra025028 0.529060666 0.43451762 0.7575619
## Bra024102 0.265003145 0.55203671 0.8257882
## Bra003687 0.745805655 0.69646755 0.5001267
## Bra011132 0.623840494 0.89460824 0.7304319
## Bra030671 0.337996932 0.82421233 0.8884395
## Bra035634 0.143252608 0.68779033 0.5748571
## Bra015961 0.383565110 0.35697767 0.7841560
## Bra023460 0.732493541 0.82645258 0.5395703
## Bra029614 0.877507264 0.56672386 0.4303039
## Bra009136 0.718510922 0.67453718 0.7276493
## Bra012492 0.815150427 0.68120040 0.5549990
## Bra003126 0.466662289 0.80211023 0.8633428
## Bra008302 0.592631484 0.60656375 0.5726884
## Bra006291 0.629122515 0.79886688 0.5799490
## Bra030155 0.843753485 0.54966565 0.3502931
## Bra000111 0.688341417 0.59073328 0.3669020
## Bra007141 0.889454558 0.45259917 0.3372403
## Bra004735 0.637799058 0.71191312 0.5044975
## Bra008561 0.157219111 0.61858807 0.5675690
## Bra011759 0.649908893 0.60816047 0.5292629
## Bra017474 0.444122788 0.91113691 0.8008811
## Bra033648 0.517680864 0.47225678 0.7136983
## Bra032105 0.422029563 0.81452686 0.8855238
## Bra019307 0.556140319 0.81010523 0.7097681
## Bra017855 0.777081556 0.66565242 0.3908589
## Bra035917 0.548849033 0.10680483 0.4966432
## Bra040320 0.632670492 0.82847666 0.6970566
## Bra000292 0.105008711 0.49275551 0.5776160
## Bra018935 0.144923591 0.61643878 0.6457904
## Bra038432 0.672892594 0.55622241 0.6388510
## Bra004749 0.458975559 0.44909678 0.7250782
## Bra022802_Bra022803 0.385289360 0.82468584 0.8090711
## Bra020472 0.328227944 0.45616431 0.8760195
## Bra007864 0.759082434 0.70117134 0.5867410
## Bra035732 0.442978397 0.66049632 0.8223090
## Bra012899 0.588740571 0.34999112 0.6715433
## Bra100459 0.730692677 0.65075246 0.3060032
## Bra017619 0.339661168 0.43350763 0.6864512
## Bra039004 0.616486439 0.67284098 0.8524644
## Bra013115 0.531879461 0.67962827 0.4790648
## Bra035117 0.415725655 0.84845681 0.8823355
## Bra027257 0.486536316 0.27565916 0.6355398
## Bra005743 0.664418248 0.39164686 0.6931359
## Bra005564 0.543245839 0.82654181 0.8599680
## Bra006850 0.336613836 0.49383618 0.6163213
## Bra028478 0.748708873 0.58061765 0.5487129
## Bra019537 0.723567610 0.60602862 0.6460898
## Bra033331 0.567133864 0.75751682 0.8096437
## Bra017224 0.707651636 0.65915406 0.6151186
## Bra013678 0.364524046 0.52912412 0.8557781
## Bra005033 0.326207908 0.72184280 0.4971892
## Bra024311 0.578897315 0.83252692 0.6192621
## Bra000090 0.795955759 0.48612808 0.4316679
## Bra027925 0.564884382 0.93905197 0.6966697
## Bra009773 0.708908984 0.67073425 0.4847198
## Bra011249 0.529006006 0.79567186 0.8396181
## Bra033980 0.576448431 0.74230014 0.3246976
## Bra018785 0.610348398 0.74840127 0.7843619
## Bra033526 0.779883289 0.38344839 0.5310336
## Bra018311 0.295878332 0.77762082 0.8980965
## Bra027681 0.293169141 0.56353638 0.8440282
## Bra033063 0.727914531 0.65533305 0.7003386
## Bra028893 0.651363364 0.60025528 0.6692401
## Bra014225 0.497968263 0.67946851 0.5752503
## Bra001697 0.759437519 0.71208454 0.5983859
## Bra004491 0.049994886 0.13716203 0.6630791
## Bra007904 0.035002210 0.26898397 0.6788862
## Bra003007 0.174248439 0.75532000 0.7755553
## Bra016266 0.709606632 0.58922689 0.6828729
## Bra020301 0.362270796 0.50960404 0.8252127
## Bra038585 0.416597713 0.19005136 0.7232679
## Bra003699 0.245189728 0.23850350 0.7069483
## Bra020697 0.442769223 0.87437897 0.6215877
## Bra031737 0.826526161 0.65085626 0.5975539
## Bra101146 0.375821761 0.46246468 0.8496130
## Bra000778 0.842514852 0.59976576 0.3651848
## Bra019179 0.844100601 0.56755492 0.4282050
## Bra023084 0.321374225 0.68554746 0.7930925
## Bra102601 0.410608903 0.83750071 0.9025638
## Bra021171 0.750520295 0.82445606 0.5345365
## Bra012890 0.476489985 0.53458273 0.8681425
## Bra029589 0.748194000 0.57991066 0.6638673
## Bra031389 0.280925121 0.84461988 0.7630917
## Bra026669 0.716759028 0.60683919 0.6415075
## Bra007279 0.476563965 0.68243439 0.8774587
## Bra023526 0.771834785 0.71959244 0.5786079
## Bra036637 0.439685045 0.84224430 0.8276690
## Bra010171 0.688560841 0.80604174 0.6511097
## Bra027717 0.812679647 0.67853837 0.5068111
## Bra019200 0.366954866 0.65848321 0.8281676
## Bra009841 0.782102229 0.62273314 0.2265424
## Bra009711 0.456491184 0.70834033 0.7974996
## Bra024238 0.880200084 0.58446774 0.3150316
## Bra024074 0.663779257 0.30080323 0.5922688
## Bra032409 0.492020665 0.70971669 0.8010028
## Bra005221 0.362163684 0.86690257 0.8462455
## Bra016147 0.683550063 0.73126535 0.6238660
## Bra037743 0.277307064 0.28008840 0.7526018
## Bra029875 0.476983734 0.85031610 0.7594547
## Bra010360 0.627628161 0.41537023 0.7243477
## Bra016300 0.714635151 0.74749189 0.5311199
## Bra018424 0.724240023 0.68862485 0.6580910
## Bra025383 0.565089362 0.69806872 0.8223021
## Bra019095 0.557440784 0.79804948 0.8481861
## Bra016683 0.575067136 0.37362035 0.6149647
## Bra016964 0.248550085 0.36185047 0.8307781
## Bra017160 0.819993562 0.43283029 0.5027028
## Bra002189 0.271719591 0.44227413 0.5776824
## Bra029880 0.324901419 0.52330365 0.8372972
## Bra013684 -0.009558235 0.22844640 0.7012858
## Bra033822 0.370393856 0.48786873 0.7665060
## Bra031841 0.197861630 0.80946022 0.8681636
## Bra038746 0.711370432 0.77766465 0.5828614
## Bra012218 0.814126407 0.57256077 0.3866381
## Bra023383 0.743953327 0.69250002 0.5919241
## Bra001819 0.357659468 0.80461860 0.8648003
## Bra030429 0.277836572 0.87177893 0.8276307
## Bra001774 0.347618875 0.50561761 0.6627837
## Bra020672 0.785887203 0.60533326 0.5636650
## Bra009854 0.779464563 0.31211091 0.4647451
## Bra023576 0.507532982 0.89651167 0.7233173
## Bra027940 0.392141209 0.27230473 0.5622872
## Bra007886 0.213520952 0.19805382 0.5608223
## Bra029387 0.337078722 0.71352994 0.5463056
## Bra038567 0.302099423 0.45354904 0.8443656
## Bra019265 0.347701517 0.34436400 0.7735258
## Bra032747 0.463940517 0.31074287 0.7559914
## Bra003670 0.329073429 0.24320821 0.6678894
## Bra037877 0.481022911 0.34363685 0.6875769
## Bra001921 0.020737839 0.41525335 0.8029842
## Bra035015 0.806431311 0.54912177 0.4846033
## Bra019398 0.295840309 0.66974475 0.4871867
## Bra038899 0.005502096 0.14315301 0.5059383
## Bra035778 0.696524351 0.64213739 0.4540671
## Bra029414 0.172423275 0.24626119 0.7429932
## Bra029039 0.288161668 0.56851584 0.9020698
## Bra006985 0.355666341 0.84573492 0.8787882
## Bra011349 0.616921949 0.55855326 0.2895196
## Bra026022 0.572436553 0.61695231 0.8135412
## Bra015704 0.482339171 0.39391439 0.8204254
## Bra037731 0.471163190 0.24228027 0.6425106
## Bra020799 0.656670388 0.80510882 0.6534058
## Bra035641 0.395129123 0.63227501 0.9029328
## Bra024935 0.697414308 0.74438697 0.5909966
## Bra023130 0.155792312 0.18533675 0.7521901
## Bra001642 0.711874603 0.81684134 0.5708803
## Bra010085 0.500602376 0.61878719 0.8770201
## Bra004946 0.582931876 0.80722554 0.6074979
## Bra025359 0.739756162 0.73433133 0.4506502
## Bra034030 0.211472333 0.49273268 0.8809104
## Bra008371 0.471693662 0.47518583 0.8080813
## Bra009840 0.794153617 0.72024929 0.4906999
## Bra013657 0.307445877 0.28415332 0.7745248
## Bra015694 0.573851874 0.87032122 0.8123514
## Bra005735 0.692171658 0.76222286 0.5423117
## Bra022827 0.218185626 0.53408421 0.8085213
## Bra018209 0.504419628 0.53167218 0.8179300
## Bra024459 0.489639292 0.12018515 0.6313631
## Bra016498 0.468364318 0.63748103 0.8193368
## Bra028150 0.816363095 0.66092680 0.6138234
## Bra038785 0.167267850 0.24276285 0.7678711
## Bra023802 0.744325176 0.57713852 0.7104224
## Bra006293 0.718875465 0.62579611 0.7115264
## Bra028523 0.102554125 0.42936841 0.8535524
## Bra000754 0.299672610 0.31719536 0.8208178
## Bra038321 0.626597155 0.77981047 0.7038346
## Bra019742 0.812074268 0.30443314 0.1369484
## Bra031771 0.643365397 0.64403596 0.6516454
## Bra019357 0.418092611 0.44766516 0.8235766
## Bra011961 0.551332371 0.90839646 0.6913047
## Bra024675 0.700399897 0.44623259 0.6395092
## Bra008780 0.355025210 0.73580396 0.6839140
## Bra010283 0.158969336 0.16275709 0.7504476
## Bra015323 0.795331782 0.71154363 0.5658203
## Bra005469 0.402924189 0.55231070 0.6520721
## Bra012607 0.542343078 0.90390513 0.5450614
## Bra034140 0.819318136 0.53679889 0.6105891
## Bra000534 0.471939902 0.74793435 0.8825970
## Bra012597 0.510605593 0.58961455 0.7837548
## Bra028400 0.695734911 0.57819763 0.6509777
## Bra030116 0.756596407 0.72511300 0.6618821
## Bra004581 0.682323033 0.62522724 0.3187978
## Bra009182 0.291830894 0.17239723 0.6912816
## Bra101149 0.629270147 0.81117877 0.7141401
## Bra027206 0.556153776 0.52843304 0.7498699
## Bra006173 0.456654610 0.78315090 0.7249966
## Bra003598 Bra016182 Bra013164
## Bra010821 0.360318245 0.57846381 0.701922906
## Bra033034 0.101487612 0.38633216 0.657339919
## Bra035334 0.649204559 0.53443737 0.270767720
## Bra003598 0.000000000 0.40086754 -0.051339262
## Bra016182 0.400867539 0.00000000 0.619988467
## Bra013164 -0.051339262 0.61998847 0.000000000
## Bra009406 0.359722220 0.82518438 0.764265326
## Bra033856 0.302209773 0.57560282 0.737583980
## Bra011196 0.696296015 0.72443515 0.351421520
## Bra041036 0.458059200 0.49217964 0.499640254
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## Bra037664 0.410918234 0.54149775 0.692086589
## Bra002697 0.701647612 0.70255013 0.465757321
## Bra025547 0.819123258 0.26966010 -0.291999618
## Bra016316 0.382464446 0.64332399 0.678814261
## Bra019741 0.231664055 0.86051061 0.791650304
## Bra020500 0.045857763 0.63040348 0.942137909
## Bra005176 0.186900845 0.66802520 0.888587349
## Bra036334 -0.141399045 0.42300231 0.905334100
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## Bra011670 0.776304714 0.51959188 0.197872403
## Bra038908 0.120960586 0.45348295 0.825776833
## Bra027181 -0.110807768 0.52602364 0.925414370
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## Bra010292 0.243876024 0.62116899 0.503896590
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## Bra038899 0.16368512 0.603476221 0.2775506 0.6141295
## Bra035778 0.83792808 0.217366310 0.6612829 0.6634361
## Bra029414 0.12755850 0.767673997 0.5280805 0.6637467
## Bra029039 0.31455978 0.673050435 0.7106749 0.8152231
## Bra006985 0.41035814 0.469910912 0.8065196 0.6436744
## Bra011349 0.75130987 0.024814438 0.5385463 0.5078677
## Bra026022 0.45926216 0.644671100 0.7407022 0.7992486
## Bra015704 0.27604229 0.831957446 0.6833227 0.8694390
## Bra037731 0.32039650 0.528415162 0.4887895 0.6190345
## Bra020799 0.69601608 0.332889776 0.8618665 0.7933300
## Bra035641 0.40236651 0.738399921 0.7960608 0.8935040
## Bra024935 0.74115288 0.291401797 0.7783180 0.7039521
## Bra023130 0.01769330 0.926077667 0.4902003 0.7043873
## Bra001642 0.70336707 0.239352174 0.8222562 0.6414002
## Bra010085 0.41559113 0.766954782 0.8011334 0.8867973
## Bra004946 0.69155237 0.235229194 0.7158662 0.5875690
## Bra025359 0.73850269 0.131111348 0.7420509 0.5766117
## Bra034030 0.17596549 0.775149474 0.6838335 0.7889757
## Bra008371 0.39804764 0.802596476 0.7292206 0.8509912
## Bra009840 0.86454094 0.237926350 0.7899515 0.6152633
## Bra013657 0.13687626 0.909884970 0.5588325 0.7290013
## Bra015694 0.67211551 0.459745323 0.8840295 0.7627999
## Bra005735 0.61760126 0.158864743 0.6928101 0.4854224
## Bra022827 0.08591852 0.771101955 0.7345429 0.7246847
## Bra018209 0.42552238 0.710651943 0.7291143 0.9155333
## Bra024459 0.09844635 0.735001835 0.4458363 0.6487872
## Bra016498 0.46494930 0.629963955 0.7631669 0.7351860
## Bra028150 0.62378890 0.484664760 0.7956477 0.7318967
## Bra038785 0.03147005 0.847390383 0.5138233 0.7218468
## Bra023802 0.58326417 0.679924278 0.8286836 0.8557159
## Bra006293 0.54679751 0.501704111 0.8425674 0.7777093
## Bra028523 0.17826663 0.781110787 0.6102221 0.7260069
## Bra000754 0.21319302 0.857864654 0.5994245 0.7949248
## Bra038321 0.55641938 0.479640294 0.8470855 0.7227197
## Bra019742 0.68914625 0.005489727 0.3870659 0.3816649
## Bra031771 0.75573831 0.337472747 0.7112424 0.7296202
## Bra019357 0.20136157 0.847180411 0.7058270 0.7935294
## Bra011961 0.68468486 0.385884876 0.8474335 0.6926584
## Bra024675 0.46409141 0.725859978 0.7822543 0.8129553
## Bra008780 0.34449999 0.391209030 0.7911762 0.5515727
## Bra010283 -0.05137313 0.864638068 0.4731313 0.6786241
## Bra015323 0.68125233 0.276782708 0.7889409 0.6601497
## Bra005469 0.15851001 0.521946646 0.6600162 0.5253801
## Bra012607 0.72959476 0.090699869 0.8044805 0.5608021
## Bra034140 0.64425275 0.546095700 0.8141292 0.8119192
## Bra000534 0.49288024 0.703840104 0.8356192 0.8411887
## Bra012597 0.40739576 0.586124523 0.8148304 0.8022742
## Bra028400 0.51826303 0.414615894 0.7643167 0.6666333
## Bra030116 0.64736009 0.404892941 0.8307797 0.7702244
## Bra004581 0.00000000 0.079916569 0.6277378 0.4727288
## Bra009182 0.07991657 0.000000000 0.5120791 0.7034552
## Bra101149 0.62773781 0.512079111 0.0000000 0.8196899
## Bra027206 0.47272879 0.703455169 0.8196899 0.0000000
## Bra006173 0.62799789 0.397686700 0.7622747 0.7895354
## Bra006173
## Bra010821 0.4566546
## Bra033034 0.7831509
## Bra035334 0.7249966
## Bra003598 0.3107548
## Bra016182 0.3504912
## Bra013164 0.5093206
## Bra009406 0.3426941
## Bra033856 0.8195789
## Bra011196 0.5604836
## Bra041036 0.7728344
## Bra011170 0.4763113
## Bra037664 0.8267056
## Bra002697 0.6115987
## Bra025547 0.2999339
## Bra016316 0.7690155
## Bra019741 0.4436502
## Bra020500 0.4181577
## Bra005176 0.5706760
## Bra036334 0.6637884
## Bra013340 0.5791303
## Bra011670 0.7068744
## Bra038908 0.6271950
## Bra027181 0.6895753
## Bra018722 0.4547610
## Bra002896 0.9088470
## Bra010292 0.6281937
## Bra021913 0.8543874
## Bra011195 0.4902227
## Bra007907_Bra007908_Bra007909 0.7556141
## Bra027700 0.6193755
## Bra036607 0.8125406
## Bra002515 0.7656568
## Bra031658 0.6402733
## Bra004810 0.7705970
## Bra005070 0.4924602
## Bra035502 0.7100553
## Bra004892 0.8724468
## Bra018386 0.8102369
## Bra040840 0.6650116
## Bra024269 0.4392574
## Bra040801 0.4914558
## Bra017219 0.7452312
## Bra022378 0.4468352
## Bra006092 0.6766925
## Bra032375 0.8040554
## Bra024197 0.7769936
## Bra023827 0.7828509
## Bra021506 0.7339621
## Bra036155 0.6502210
## Bra013676_Bra013677 0.6385745
## Bra036852 0.7255844
## Bra005071 0.5130406
## Bra014819 0.5668426
## Bra013682 0.4370243
## Bra013628 0.6581462
## Bra037283 0.5125382
## Bra016610 0.9238522
## Bra011606 0.7427339
## Bra004130 0.6120931
## Bra036217 0.8069006
## Bra015896 0.8357231
## Bra022342 0.8492853
## Bra005227 0.3524877
## Bra031068 0.7016299
## Bra006273 0.6190225
## Bra020646 0.4841422
## Bra017113 0.5485973
## Bra034676 0.4356669
## Bra006683 0.7024938
## Bra025028 0.5103257
## Bra024102 0.5559771
## Bra003687 0.5190571
## Bra011132 0.8515432
## Bra030671 0.8165970
## Bra035634 0.6881942
## Bra015961 0.5151436
## Bra023460 0.7454616
## Bra029614 0.4676773
## Bra009136 0.7937820
## Bra012492 0.6061013
## Bra003126 0.8284213
## Bra008302 0.8343888
## Bra006291 0.8200052
## Bra030155 0.5196560
## Bra000111 0.7349104
## Bra007141 0.6020218
## Bra004735 0.8377314
## Bra008561 0.7452299
## Bra011759 0.3873047
## Bra017474 0.8166600
## Bra033648 0.5015676
## Bra032105 0.8582706
## Bra019307 0.6936871
## Bra017855 0.6983628
## Bra035917 0.1158546
## Bra040320 0.8872848
## Bra000292 0.6955268
## Bra018935 0.8451440
## Bra038432 0.6038193
## Bra004749 0.6644221
## Bra022802_Bra022803 0.7042752
## Bra020472 0.7163266
## Bra007864 0.6751152
## Bra035732 0.5985713
## Bra012899 0.4048424
## Bra100459 0.7121009
## Bra017619 0.4611080
## Bra039004 0.7730938
## Bra013115 0.6871481
## Bra035117 0.7572348
## Bra027257 0.3078758
## Bra005743 0.5762985
## Bra005564 0.9151348
## Bra006850 0.5201132
## Bra028478 0.5895944
## Bra019537 0.5733431
## Bra033331 0.7170637
## Bra017224 0.8111887
## Bra013678 0.7141037
## Bra005033 0.8943511
## Bra024311 0.6745144
## Bra000090 0.6482501
## Bra027925 0.8095275
## Bra009773 0.7545233
## Bra011249 0.7444649
## Bra033980 0.7803442
## Bra018785 0.8253903
## Bra033526 0.6506501
## Bra018311 0.6390696
## Bra027681 0.5977494
## Bra033063 0.6612042
## Bra028893 0.6068921
## Bra014225 0.8783451
## Bra001697 0.7017729
## Bra004491 0.5522139
## Bra007904 0.3713264
## Bra003007 0.7663605
## Bra016266 0.6196672
## Bra020301 0.5870500
## Bra038585 0.5017292
## Bra003699 0.5288715
## Bra020697 0.8478445
## Bra031737 0.7830135
## Bra101146 0.6944088
## Bra000778 0.6497193
## Bra019179 0.6326480
## Bra023084 0.5286459
## Bra102601 0.8832125
## Bra021171 0.7382608
## Bra012890 0.6284932
## Bra029589 0.5431698
## Bra031389 0.6091425
## Bra026669 0.4870348
## Bra007279 0.7942652
## Bra023526 0.7911694
## Bra036637 0.8486626
## Bra010171 0.8983378
## Bra027717 0.6979556
## Bra019200 0.8079060
## Bra009841 0.4906905
## Bra009711 0.8426100
## Bra024238 0.6392557
## Bra024074 0.2938647
## Bra032409 0.9400803
## Bra005221 0.7423761
## Bra016147 0.7562163
## Bra037743 0.3052560
## Bra029875 0.9012659
## Bra010360 0.4694120
## Bra016300 0.8079975
## Bra018424 0.8599371
## Bra025383 0.8695672
## Bra019095 0.8887908
## Bra016683 0.2659011
## Bra016964 0.6257342
## Bra017160 0.5003476
## Bra002189 0.4812762
## Bra029880 0.5014472
## Bra013684 0.3648959
## Bra033822 0.6141798
## Bra031841 0.8435471
## Bra038746 0.7606175
## Bra012218 0.6539363
## Bra023383 0.6853590
## Bra001819 0.7800714
## Bra030429 0.7218634
## Bra001774 0.3073046
## Bra020672 0.5763460
## Bra009854 0.4525297
## Bra023576 0.9148105
## Bra027940 0.3426656
## Bra007886 0.5792834
## Bra029387 0.9217962
## Bra038567 0.6250561
## Bra019265 0.5056421
## Bra032747 0.4170157
## Bra003670 0.2330465
## Bra037877 0.4156773
## Bra001921 0.4599415
## Bra035015 0.8017774
## Bra019398 0.8518513
## Bra038899 0.5771409
## Bra035778 0.8295968
## Bra029414 0.3318867
## Bra029039 0.7196554
## Bra006985 0.7634967
## Bra011349 0.7613037
## Bra026022 0.7675442
## Bra015704 0.6146709
## Bra037731 0.4076545
## Bra020799 0.9151242
## Bra035641 0.7799215
## Bra024935 0.8330027
## Bra023130 0.3800336
## Bra001642 0.7682794
## Bra010085 0.7898990
## Bra004946 0.8791458
## Bra025359 0.7353028
## Bra034030 0.6427212
## Bra008371 0.6672071
## Bra009840 0.6941554
## Bra013657 0.4919301
## Bra015694 0.8705385
## Bra005735 0.6919703
## Bra022827 0.5078756
## Bra018209 0.8398857
## Bra024459 0.3107374
## Bra016498 0.7074590
## Bra028150 0.7500315
## Bra038785 0.4238503
## Bra023802 0.7160536
## Bra006293 0.6593423
## Bra028523 0.5085055
## Bra000754 0.5237392
## Bra038321 0.7202542
## Bra019742 0.5264577
## Bra031771 0.8051955
## Bra019357 0.5372517
## Bra011961 0.8953396
## Bra024675 0.5378318
## Bra008780 0.4945323
## Bra010283 0.3310019
## Bra015323 0.7762572
## Bra005469 0.4083062
## Bra012607 0.7793429
## Bra034140 0.6454269
## Bra000534 0.8647399
## Bra012597 0.5850821
## Bra028400 0.5534101
## Bra030116 0.7863303
## Bra004581 0.6279979
## Bra009182 0.3976867
## Bra101149 0.7622747
## Bra027206 0.7895354
## Bra006173 0.0000000# 2 means cols, 1 means rows
GxE_rank <- apply(GxE_cor,2,function(x) rank(-abs(x)))
# rank for each column from high to low
GxE_MR <- sqrt(GxE_rank * t(GxE_rank))
GxE_MR## Bra010821 Bra033034 Bra035334 Bra003598
## Bra010821 255.000000 195.345847 235.053185 173.651951
## Bra033034 195.345847 255.000000 135.222040 245.385411
## Bra035334 235.053185 135.222040 255.000000 96.607453
## Bra003598 173.651951 245.385411 96.607453 255.000000
## Bra016182 107.958325 217.292430 172.409396 174.298594
## Bra013164 69.195376 101.143462 219.909072 243.495380
## Bra009406 28.284271 163.694838 212.781578 186.021504
## Bra033856 163.908511 26.720778 109.087121 209.570990
## Bra011196 100.950483 233.518736 132.815662 72.477583
## Bra041036 223.492729 32.863353 31.016125 167.570881
## Bra011170 194.699769 208.925824 62.833112 149.197855
## Bra037664 147.122398 35.411862 93.568157 178.280678
## Bra002697 56.497788 206.240151 152.990196 80.727938
## Bra025547 239.897895 240.120803 80.622577 18.027756
## Bra016316 168.288443 36.055513 99.839872 192.732976
## Bra019741 83.066239 121.490740 205.669638 222.890107
## Bra020500 22.271057 135.716617 231.594473 244.499489
## Bra005176 11.618950 155.177318 220.454077 221.918904
## Bra036334 87.948849 76.302031 217.508621 221.918904
## Bra013340 181.052479 181.659021 38.987177 52.915026
## Bra011670 199.607114 165.915641 8.831761 49.173163
## Bra038908 35.916570 141.449638 223.492729 227.964910
## Bra027181 113.736538 45.000000 209.833267 231.980603
## Bra018722 232.826115 231.447618 70.000000 28.248894
## Bra002896 150.039995 61.237244 119.895788 196.061215
## Bra010292 227.389534 75.835348 80.124902 225.619148
## Bra021913 204.440700 146.331815 24.372115 103.884551
## Bra011195 116.189500 132.261105 152.672853 179.963885
## Bra007907_Bra007908_Bra007909 233.987179 143.164241 1.414214 103.072790
## Bra027700 229.455878 210.499406 41.952354 56.026779
## Bra036607 215.350876 143.248037 7.071068 89.397987
## Bra002515 93.166518 74.357246 145.657132 143.499129
## Bra031658 160.112460 148.148574 102.825094 171.473030
## Bra004810 185.369900 13.416408 112.463327 224.499443
## Bra005070 224.997778 224.891085 50.645829 27.129320
## Bra035502 22.583180 137.477271 214.158820 220.336107
## Bra004892 120.863559 94.286797 122.081940 196.692654
## Bra018386 162.619187 203.661484 65.726707 78.409183
## Bra040840 58.309519 134.387499 168.789810 139.104277
## Bra024269 210.399620 211.962261 74.833148 121.016528
## Bra040801 235.265807 220.549314 78.555713 57.991379
## Bra017219 232.140044 38.496753 10.954451 174.112033
## Bra022378 217.453443 232.344572 61.016391 10.677078
## Bra006092 242.794151 121.667580 28.530685 217.680959
## Bra032375 81.387960 122.163824 162.763632 199.198394
## Bra024197 172.087187 12.000000 72.890329 197.149689
## Bra023827 147.770092 21.071308 73.450664 177.617567
## Bra021506 67.082039 65.726707 189.208879 224.109348
## Bra036155 30.199338 97.918333 221.912145 244.495399
## Bra013676_Bra013677 207.846097 192.468179 33.911650 32.726136
## Bra036852 57.965507 111.539231 197.936859 200.723691
## Bra005071 228.997817 222.454490 48.836462 34.583233
## Bra014819 8.717798 165.227116 221.810730 203.754755
## Bra013682 201.499380 231.922401 59.514704 1.732051
## Bra013628 206.688171 166.418148 3.464102 77.071395
## Bra037283 231.499460 188.618663 51.652686 49.959984
## Bra016610 176.295207 106.235587 104.976188 173.637554
## Bra011606 115.321290 54.415071 186.263255 234.473879
## Bra004130 194.976922 200.494389 63.450768 37.229021
## Bra036217 200.000000 75.993421 9.165151 128.685664
## Bra015896 142.478068 20.712315 93.096724 173.124233
## Bra022342 199.959996 2.000000 72.415468 219.963633
## Bra005227 245.458754 219.692968 89.777503 63.498031
## Bra031068 116.309931 96.467611 137.695316 197.370211
## Bra006273 37.788887 106.620823 208.494604 232.473654
## Bra020646 240.898319 147.380460 95.979164 206.058244
## Bra017113 80.603970 150.917196 209.138710 234.863790
## Bra034676 237.924358 206.842936 60.663004 54.552727
## Bra006683 138.039849 14.832397 124.330206 203.004926
## Bra025028 150.000000 203.396165 75.775986 17.320508
## Bra024102 234.989361 172.510869 21.748563 175.057134
## Bra003687 59.749477 98.005102 203.228935 200.624026
## Bra011132 131.871149 16.970563 121.453695 208.830074
## Bra030671 220.667170 41.821047 14.071247 155.190206
## Bra035634 242.495361 41.121770 111.933016 252.495545
## Bra015961 187.082869 211.485224 65.268675 22.978251
## Bra023460 77.627315 46.151923 190.682983 227.257563
## Bra029614 3.872983 150.970196 216.245231 175.134234
## Bra009136 93.241622 136.381817 124.715677 168.961534
## Bra012492 27.239677 112.463327 193.494186 191.261601
## Bra003126 191.159619 58.957612 30.331502 145.106857
## Bra008302 124.671569 143.248037 176.657861 220.454077
## Bra006291 118.583304 57.549978 180.493767 240.270681
## Bra030155 7.483315 147.427949 216.076375 188.865031
## Bra000111 79.372539 134.342845 212.967134 241.991735
## Bra007141 2.645751 179.131237 221.348142 177.186343
## Bra004735 110.118118 89.916628 196.967002 233.638610
## Bra008561 241.474636 86.162637 131.491445 245.900386
## Bra011759 90.553851 128.965112 185.817114 193.411478
## Bra017474 191.468013 7.348469 65.482822 182.745725
## Bra033648 153.049012 194.743421 63.796552 55.389530
## Bra032105 200.624026 47.696960 17.320508 155.579562
## Bra019307 149.969997 45.923850 117.447861 202.326469
## Bra017855 43.485630 103.498792 206.048538 225.486141
## Bra035917 103.773792 244.899980 157.607106 10.954451
## Bra040320 125.139922 41.327957 137.386317 215.784615
## Bra000292 244.991837 138.394364 103.585713 254.000000
## Bra018935 241.991735 91.214034 84.982351 234.345898
## Bra038432 100.687636 179.092155 160.996894 179.532727
## Bra004749 190.021051 215.109275 51.497573 191.049732
## Bra022802_Bra022803 203.926457 32.465366 50.368641 202.464812
## Bra020472 212.936610 195.836667 23.473389 41.533119
## Bra007864 59.093147 105.066646 182.482876 221.479119
## Bra035732 187.531331 127.530389 40.558600 103.720779
## Bra012899 122.674366 226.682597 106.634891 78.974679
## Bra100459 57.766772 107.359210 215.053482 248.000000
## Bra017619 204.648479 190.352305 52.649786 99.839872
## Bra039004 144.665131 142.481578 39.572718 120.631671
## Bra013115 143.902745 98.919159 202.200396 249.967998
## Bra035117 202.694351 28.913665 21.494185 177.808886
## Bra027257 153.267740 235.410280 109.416635 87.086164
## Bra005743 96.524608 218.670986 109.840794 53.028294
## Bra005564 167.511194 49.355851 36.986484 157.759310
## Bra006850 214.615936 170.334964 85.246701 207.987980
## Bra028478 52.153619 160.299719 194.483932 196.356818
## Bra019537 72.828566 164.097532 162.849624 135.025923
## Bra033331 159.097454 84.805660 66.932802 163.082801
## Bra017224 90.746901 132.680066 174.928557 188.547076
## Bra013678 206.809091 179.248431 33.674916 57.861905
## Bra005033 198.494332 51.613952 171.624590 250.000000
## Bra024311 132.966161 22.649503 161.369142 235.219047
## Bra000090 26.944387 180.482686 210.466149 206.164982
## Bra027925 146.645832 2.828427 133.760981 222.364566
## Bra009773 80.498447 111.552678 200.192407 230.824609
## Bra011249 168.748333 62.609903 42.848571 136.586969
## Bra033980 114.254103 63.992187 207.699302 233.473767
## Bra018785 141.357702 87.669835 82.401456 137.985506
## Bra033526 30.397368 224.430390 198.317927 138.585714
## Bra018311 228.582589 58.326666 10.816654 143.115338
## Bra027681 225.969024 167.496269 17.748239 149.542636
## Bra033063 81.332650 143.300384 136.733317 126.554336
## Bra028893 113.841996 161.925909 144.353732 170.340835
## Bra014225 155.589203 96.498705 168.142796 242.833276
## Bra001697 62.888791 105.337553 184.255258 200.648947
## Bra004491 244.458585 233.452351 82.849261 54.313902
## Bra007904 249.495491 208.393858 67.749539 73.006849
## Bra003007 242.833276 47.968740 43.301270 193.695638
## Bra016266 89.246849 170.798126 145.044821 146.969385
## Bra020301 202.464812 184.304097 45.497253 67.823300
## Bra038585 172.765737 243.000000 78.409183 3.872983
## Bra003699 229.434086 236.499471 26.495283 123.207143
## Bra020697 180.410643 8.831761 157.213231 247.414632
## Bra031737 23.430749 136.352484 181.901072 166.514264
## Bra101146 202.205341 199.108011 35.916570 48.764741
## Bra000778 16.492423 133.906684 216.711790 220.855156
## Bra019179 9.486833 154.492718 218.814990 219.349037
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## Bra031068 195.943870 9.165151 124.715677 134.461891
## Bra006273 246.499493 125.419297 204.381995 143.579246
## Bra020646 71.728655 107.359210 60.099917 124.402572
## Bra017113 234.380033 137.094858 209.721244 166.871208
## Bra034676 35.071356 161.570418 81.914590 182.887944
## Bra006683 218.013761 50.199602 195.391914 121.045446
## Bra025028 58.094750 109.361785 62.498000 191.447121
## Bra024102 131.400152 110.272390 95.320512 181.975273
## Bra003687 229.041481 82.060953 201.910871 187.957442
## Bra011132 206.378293 31.701735 143.321317 42.720019
## Bra030671 131.144958 35.071356 64.899923 50.517324
## Bra035634 191.906227 105.470375 117.473401 46.861498
## Bra015961 14.282857 137.619039 58.966092 175.727061
## Bra023460 233.345238 60.158125 176.592752 102.601170
## Bra029614 192.382432 81.166496 192.301846 205.757138
## Bra009136 159.705980 28.982753 40.926764 75.206383
## Bra012492 208.278659 56.480085 166.499249 166.925133
## Bra003126 162.277540 60.761830 95.498691 48.145612
## Bra008302 204.660695 137.083916 95.393920 28.372522
## Bra006291 225.625796 47.370877 133.865604 47.486840
## Bra030155 201.799405 127.890578 206.533290 169.826382
## Bra000111 249.000000 156.204994 171.665372 84.409715
## Bra007141 218.247566 159.047163 173.505043 142.028166
## Bra004735 235.694718 85.866175 118.473626 31.464265
## Bra008561 223.150174 124.955992 131.578874 28.301943
## Bra011759 218.084846 74.913283 210.190390 222.676896
## Bra017474 189.971050 37.523326 142.968528 49.507575
## Bra033648 18.761663 88.266641 75.166482 198.469141
## Bra032105 136.802778 22.181073 50.833060 31.464265
## Bra019307 209.133928 101.350876 205.844602 126.747781
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## Bra040320 198.944716 14.142136 55.497748 13.964240
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## Bra038432 200.237359 102.332790 115.982757 170.812763
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## Bra012899 131.419177 122.906469 100.950483 229.980434
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## Bra017619 15.652476 112.529996 89.162773 192.631773
## Bra039004 100.727355 9.165151 6.000000 96.850400
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## Bra035117 155.537777 41.231056 135.277493 93.230896
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## Bra005564 157.556339 23.685439 57.549978 8.485281
## Bra006850 129.799846 104.441371 57.827329 157.765649
## Bra028478 211.452122 94.915752 119.795659 168.493323
## Bra019537 143.331783 20.445048 69.885621 190.787840
## Bra033331 140.413675 14.832397 86.585218 124.515059
## Bra017224 175.818088 84.000000 98.366661 50.299105
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## Bra005033 223.944189 102.664502 105.242577 6.633250
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## Bra027925 217.680959 39.572718 180.864590 59.598658
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## Bra033980 239.991667 141.308174 195.540277 56.000000
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## Bra033526 177.549993 161.415613 105.071404 126.142776
## Bra018311 142.407865 77.071395 162.480768 149.879952
## Bra027681 97.118484 66.992537 41.182521 166.499249
## Bra033063 170.660482 88.910067 149.231364 154.996774
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## Bra014225 206.276513 129.730490 128.124939 8.944272
## Bra001697 201.216302 39.799497 133.940285 130.476051
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## Bra003007 159.931235 147.051012 183.016393 46.946778
## Bra016266 182.153781 90.994505 124.659536 171.840042
## Bra020301 49.497475 98.868600 56.683331 163.438062
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## Bra020697 222.189109 14.866069 111.409156 21.166010
## Bra031737 183.706287 47.148701 62.457986 76.341339
## Bra101146 36.331804 130.636901 18.734994 107.624347
## Bra000778 245.000000 125.737822 170.235132 124.322162
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## Bra021171 231.689447 60.794737 165.852344 108.678425
## Bra012890 104.742542 131.476234 86.752522 165.354165
## Bra029589 132.136293 40.099875 76.485293 199.734824
## Bra031389 226.825924 89.246849 222.557858 135.646600
## Bra026669 141.414285 46.086874 148.000000 218.853833
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## Bra023526 207.552403 58.480766 123.814377 75.498344
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## Bra019200 62.449980 104.699570 67.000000 45.276926
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## Bra009711 121.749743 5.916080 1.414214 26.115130
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## Bra032409 164.383697 87.000000 23.366643 1.000000
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## Bra016147 209.630628 125.805405 181.196026 86.429162
## Bra037743 28.142495 161.369142 120.183194 219.786260
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## Bra016300 237.309924 86.382869 140.911320 59.808026
## Bra018424 163.217646 54.854353 74.229374 24.248711
## Bra025383 94.657277 57.965507 24.494897 23.874673
## Bra019095 133.985074 30.199338 46.475800 20.199010
## Bra016683 98.005102 129.042629 180.845238 242.833276
## Bra016964 12.649111 147.404206 31.811947 125.315602
## Bra017160 206.809091 145.327217 168.297356 197.909070
## Bra002189 217.788889 79.183332 43.680659 155.826827
## Bra029880 52.411831 123.089398 121.449578 196.908608
## Bra013684 27.495454 162.000000 114.786759 182.537667
## Bra033822 100.309521 76.915538 11.401754 153.460093
## Bra031841 140.790625 63.071388 69.411815 25.690465
## Bra038746 220.454077 48.662100 161.996914 99.814829
## Bra012218 234.980850 151.046351 189.799895 119.058809
## Bra023383 166.288905 15.165751 103.489130 127.937485
## Bra001819 160.159296 61.967734 117.481914 70.746025
## Bra030429 203.597642 91.531415 197.727085 87.309793
## Bra001774 103.773792 91.454907 180.524237 235.168025
## Bra020672 192.888569 58.694122 140.943251 183.670901
## Bra009854 42.402830 152.026314 124.442758 212.849712
## Bra023576 212.414689 80.237149 138.390751 8.124038
## Bra027940 132.499057 140.879381 96.343137 223.275614
## Bra007886 45.825757 169.218793 83.666003 90.332718
## Bra029387 218.888099 138.592929 126.039676 1.732051
## Bra038567 37.080992 116.747591 26.532998 140.028569
## Bra019265 31.080541 156.725875 80.249611 180.554701
## Bra032747 61.611687 163.168624 84.852814 215.076730
## Bra003670 90.912045 184.737652 171.026314 238.058816
## Bra037877 160.221721 172.249819 127.749755 224.432618
## Bra001921 135.499077 179.033516 128.382242 172.817823
## Bra035015 170.452339 122.882057 102.058807 45.891176
## Bra019398 232.499462 144.000000 114.769334 10.954451
## Bra038899 37.094474 185.175592 49.779514 62.896741
## Bra035778 227.734495 135.535973 123.838605 34.942810
## Bra029414 41.809090 164.383697 104.124925 207.975960
## Bra029039 93.541435 115.277925 39.799497 97.954071
## Bra006985 174.997143 59.447456 153.434025 80.461171
## Bra011349 250.499501 160.156174 168.448805 54.405882
## Bra026022 114.411538 108.885261 47.286362 76.485293
## Bra015704 30.886890 133.446619 14.730920 153.479640
## Bra037731 130.153755 207.376469 100.444014 226.433213
## Bra020799 205.365528 25.099801 67.527772 6.708204
## Bra035641 71.777434 73.484692 9.797959 74.899933
## Bra024935 213.766227 94.276190 125.139922 47.623524
## Bra023130 3.605551 169.289693 80.789851 190.641024
## Bra001642 221.422673 61.416610 162.499231 94.233752
## Bra010085 64.899923 72.828566 12.247449 72.249567
## Bra004946 222.560104 123.802262 177.640086 15.491933
## Bra025359 236.495243 106.301458 176.312223 99.819838
## Bra034030 47.728398 126.948809 56.124861 131.156395
## Bra008371 43.081318 108.664622 22.803509 127.499020
## Bra009840 224.278844 78.974679 165.698521 123.377470
## Bra013657 4.898979 160.071859 77.653075 175.031426
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## Bra005735 233.946575 135.277493 205.800875 121.983605
## Bra022827 36.000000 85.556999 79.523581 186.614576
## Bra018209 81.975606 114.647285 2.449490 34.409301
## Bra024459 44.362146 191.702895 108.540315 224.566249
## Bra016498 121.655251 82.401456 94.116949 119.849906
## Bra028150 167.248318 83.276647 108.995413 102.849404
## Bra038785 22.248595 168.196314 76.124897 187.576651
## Bra023802 106.094298 33.882149 13.038405 120.233107
## Bra006293 166.871208 34.770677 70.746025 158.126532
## Bra028523 42.213742 150.515780 79.812280 172.910381
## Bra000754 19.748418 158.792317 50.645829 168.374582
## Bra038321 172.162714 24.372115 101.685791 105.356538
## Bra019742 253.499507 181.659021 184.078787 132.227077
## Bra031771 204.777928 127.216351 95.278539 45.607017
## Bra019357 26.832816 122.106511 55.928526 182.989071
## Bra011961 194.043809 33.045423 121.474277 13.416408
## Bra024675 62.489999 54.543561 28.372522 189.905240
## Bra008780 189.314553 38.729833 180.416186 193.687893
## Bra010283 12.688578 175.271218 94.710084 204.264534
## Bra015323 216.076375 89.325248 148.458748 87.120606
## Bra005469 138.390751 112.249722 191.676811 224.919986
## Bra012607 242.487113 62.992063 183.915742 70.887234
## Bra034140 150.532389 41.952354 35.468296 151.525575
## Bra000534 91.531415 46.957428 32.588341 29.325757
## Bra012597 133.596407 35.242020 34.481879 181.535121
## Bra028400 190.021051 79.598995 138.426876 193.028495
## Bra030116 192.686274 51.205468 84.142736 78.993671
## Bra004581 242.997942 121.095004 186.652083 107.112091
## Bra009182 255.000000 164.048773 80.870266 191.671594
## Bra101149 164.048773 255.000000 38.729833 87.988636
## Bra027206 80.870266 38.729833 255.000000 53.768020
## Bra006173 191.671594 87.988636 53.768020 255.000000genes_adj_MR3 <- GxE_MR <= 3 # cut off 3
diag(genes_adj_MR3) <- 0
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diag(genes_adj_MR10) <- 0
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## Bra015323 0 0 0 0
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## Bra034140 0 0 0 0
## Bra000534 0 0 0 0
## Bra012597 0 0 0 0
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## Bra027206 0 0 0 0
## Bra006173 0 0 0 0sum(genes_adj_MR3)## [1] 516sum(genes_adj_MR10)## [1] 2120Exercise 7 plot networks for MR3 and MR10
gene_graphMR3 <- graph.adjacency(genes_adj_MR3, mode = "undirected") #convert adjacency to graph
comps <- clusters(gene_graphMR3)$membership #define gene cluster membership
colbar <- rainbow(max(comps)+1) #define colors
V(gene_graphMR3)$color <- colbar[comps+1] #assign colors to nodes
plot(gene_graphMR3, layout = layout.fruchterman.reingold, vertex.size = 6, vertex.label = NA)
gene_graphMR10 <- graph.adjacency(genes_adj_MR10, mode = "undirected") #convert adjacency to graph
comps <- clusters(gene_graphMR10)$membership #define gene cluster membership
colbar <- rainbow(max(comps)+1) #define colors
V(gene_graphMR10)$color <- colbar[comps+1] #assign colors to nodes
plot(gene_graphMR10, layout = layout.fruchterman.reingold, vertex.size = 6, vertex.label = NA)
Answer: MR10 has more edges such that the network looks more complicated than MR3. color = membership?
Exercise 8 graph density
graph.density(gene_graphMR10)## [1] 0.0327312average.path.length(gene_graphMR10)## [1] 4.174618We get the shortest paths between ALL genes in the network and then print the results. We are interested in visualizing the path between Bra033034 (row number 2) and Bra009406 (column number 7). This is where the 2 and 7 arguments come from in get.shortest.paths()
gene_graphMR10 <- graph.adjacency(genes_adj_MR10, mode = "undirected")
distMatrix <- shortest.paths(gene_graphMR10, v = V(gene_graphMR10), to = V(gene_graphMR10))
head(distMatrix)[,1:7]## Bra010821 Bra033034 Bra035334 Bra003598 Bra016182 Bra013164
## Bra010821 0 5 7 7 4 3
## Bra033034 5 0 4 7 5 3
## Bra035334 7 4 0 3 5 7
## Bra003598 7 7 3 0 5 8
## Bra016182 4 5 5 5 0 4
## Bra013164 3 3 7 8 4 0
## Bra009406
## Bra010821 2
## Bra033034 4
## Bra035334 6
## Bra003598 5
## Bra016182 2
## Bra013164 3pl <- get.shortest.paths(gene_graphMR10, 2, 7)$vpath[[1]] # pull paths between node 2 and 7
V(gene_graphMR10)[pl]$color <- paste("green") # define node color
E(gene_graphMR10)$color <- paste("grey") # define default edge color
E(gene_graphMR10, path = pl)$color <- paste("blue") # define edge color
E(gene_graphMR10, path = pl)$width <- 10 # define edge width
plot(gene_graphMR10, layout = layout.fruchterman.reingold, vertex.size = 6, vertex.label = NA)
Exercise 9
graph density of 1500 miles range
cities_mat## BOS NY DC MIA CHI SEA SF LA DEN
## BOS 0 1 1 0 1 0 0 0 0
## NY 1 0 1 1 1 0 0 0 0
## DC 1 1 0 1 1 0 0 0 0
## MIA 0 1 1 0 1 0 0 0 0
## CHI 1 1 1 1 0 0 0 0 1
## SEA 0 0 0 0 0 0 1 1 1
## SF 0 0 0 0 0 1 0 1 1
## LA 0 0 0 0 0 1 1 0 1
## DEN 0 0 0 0 1 1 1 1 0gene_graphcities <- graph.adjacency(cities_mat, mode = "undirected") #convert adjacency to graph
comps <- clusters(gene_graphcities)$membership #define gene cluster membership
colbar <- rainbow(max(comps)+1) #define colors
V(gene_graphcities)$color <- colbar[comps+1] #assign colors to nodes
plot(gene_graphcities, layout = layout.fruchterman.reingold, vertex.size = 6, vertex.label = NA)
graph.density(gene_graphcities)## [1] 0.4444444average.path.length(gene_graphcities)## [1] 1.888889Find shortest btw SEA and DC in 1500 range
gene_graphcities <- graph.adjacency(cities_mat, mode = "undirected")
distMatrix <- shortest.paths(gene_graphcities, v = V(gene_graphcities), to = V(gene_graphcities))
head(distMatrix)[,1:7]## BOS NY DC MIA CHI SEA SF
## BOS 0 1 1 2 1 3 3
## NY 1 0 1 1 1 3 3
## DC 1 1 0 1 1 3 3
## MIA 2 1 1 0 1 3 3
## CHI 1 1 1 1 0 2 2
## SEA 3 3 3 3 2 0 1pl <- get.shortest.paths(gene_graphcities, 6, 3)$vpath[[1]] # pull paths between node 2 and 7
V(gene_graphcities)[pl]$color <- paste("green") # define node color
E(gene_graphcities)$color <- paste("grey") # define default edge color
E(gene_graphcities, path = pl)$color <- paste("blue") # define edge color
E(gene_graphcities, path = pl)$width <- 10 # define edge width
plot(gene_graphcities, layout = layout.fruchterman.reingold, vertex.size = 6, vertex.label = NA)
Find shortest distance btw SEA and DC with 2300 mile range
gene_graphcities <- graph.adjacency(cities_mat_2300, mode = "undirected")
distMatrix <- shortest.paths(gene_graphcities, v = V(gene_graphcities), to = V(gene_graphcities))
head(distMatrix)[,1:7]## BOS NY DC MIA CHI SEA SF
## BOS 0 1 1 1 1 2 2
## NY 1 0 1 1 1 2 2
## DC 1 1 0 1 1 2 2
## MIA 1 1 1 0 1 2 2
## CHI 1 1 1 1 0 1 1
## SEA 2 2 2 2 1 0 1pl <- get.shortest.paths(gene_graphcities, 6, 3)$vpath[[1]] # pull paths between node 2 and 7
V(gene_graphcities)[pl]$color <- paste("green") # define node color
E(gene_graphcities)$color <- paste("grey") # define default edge color
E(gene_graphcities, path = pl)$color <- paste("blue") # define edge color
E(gene_graphcities, path = pl)$width <- 10 # define edge width
plot(gene_graphcities, layout = layout.fruchterman.reingold, vertex.size = 6, vertex.label = NA)